Is it permitted to eat manufactured foods that include non-kosher ingredients in quantities insignificant enough that they are batel? Hirhurim "pulled some stuff together after dinner":
Regarding whether something that one cannot taste is permissible to eat, there is a three-way disagreement among rishonim about whether something is forbidden if one cannot taste it but it is more than 1/60th of a mixture. The Rema rules strictly like Rashi, the Ramban, the Rashba and the Ran. On this, see Arukh Ha-Shulhan, Yoreh De'ah 98:21-22, 25.
R. Akiva Eiger (Glosses to Yoreh De'ah 99:5) quotes a responsum of the Rivash to the effect that someone manufacturing a foodstuff who dilutes a forbidden ingredient is diluting it on behalf of all of his customers and the mixture is therefore forbidden to anyone who buys it. This is, however, hotly disputed. The Darkhei Teshuvah (99:67, 108:20) quotes a host of posekim agreeing with R. Akiva Eiger and a host disagreeing with him. The rabbi who taught me Yoreh De'ah agreed with R. Akiva Eiger.
The upshot of these two positions is that if a manufacturer mixes a forbidden ingredient into food to the point that one cannot taste it, the mixture is forbidden to all.
I'm not sure this is quite right. R. Akiva Eiger is referring to Responsum 498 in the Rivash. The question the Rivash deals with there is (inter alia) as follows: A food item in which a forbidden ingredient has been deliberately made batel is forbidden both to the preparer (as a penalty for having been mevatel isur lechatchila) as well as to the person for whom he has prepared it. The Rivash holds that the penalty is applied to the end consumer also in a case where the preparer did not have a particular buyer in mind but simply intended to sell it on the market.
This point is relevant as far as it goes but does not deal with the question of what constitutes a deliberate act of bitul issur lechatchila. If we are going to accept the Rivash's chumrah, we might consider a closely related kulah of the Rivash. In Responsum 349, the Rivash deals with the question of wine barrels sealed with non-kosher fat. Since the fat does not mix, or even adhere, to the wine he holds there is no problem. He adds an additional point: there is no problem of ein mevatlin issur lechatchila in this case because the wine is put in the offending barrels as part of the manufacturing process and not for the purpose of being mevatel the offending fat. Thus, it may very well be that the same holds for manufactured products generally, where the manufacturer has no intent to be mevatel the issur.
(I acknowledge that in the Rivash's case, since the fat does not adhere to the wine, it could be argued that there in no mixture at all and therefore no bitul. Thus, unlike in the case of the manufactured products in question here, the issue of ein mevatlin issur lechatchila may never arise. But note that this is not what the Rivash chooses to argue.)